$L_\infty$-morphisms between twisted Courant $r$-Lie algebras and untwisted Courant $(r{+}1)$-Lie algebroids
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| Formato: | Preprint |
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2026
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| _version_ | 1866912907271340032 |
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| author | Fiorenza, Domenico Miti, Antonio Michele |
| author_facet | Fiorenza, Domenico Miti, Antonio Michele |
| contents | In "Lie infinity algebras and higher analogues of Dirac structures and Courant algebroids" [arXiv:1003.1004], Marco Zambon constructs an $L_\infty$-algebra associated with any higher standard or twisted Courant algebroid (also known as a Vinogradov algebroid), and exhibits an explicit $L_\infty$-morphism from the Lie algebra associated with a standard Lie algebroid twisted by a closed 2-form to the Lie-2 algebra of the standard Courant algebroid. He poses the question of whether analogous canonical $L_\infty$-morphisms exist in higher degrees -- namely, for any standard higher Courant algebroid twisted by a closed $(r+1)$-form. We adfirmatively answer this question, presenting a general framework that naturally yields such canonical $L_\infty$-morphisms for arbitrary $r$, while at the same time clarifying the geometrical and homotopical structures underlying the construction. We also show how this framework accommodates the canonical morphism between Roger's observable $L_\infty$-algebra of a pre-$r$-plectic manifold and the higher Courant algebra described by Zambon and one of the authors in "Observables on multisymplectic manifolds and higher Courant algebroids" [arXiv:2209.05836]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_14702 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | $L_\infty$-morphisms between twisted Courant $r$-Lie algebras and untwisted Courant $(r{+}1)$-Lie algebroids Fiorenza, Domenico Miti, Antonio Michele Symplectic Geometry Mathematical Physics Differential Geometry 53D05, 17B55 In "Lie infinity algebras and higher analogues of Dirac structures and Courant algebroids" [arXiv:1003.1004], Marco Zambon constructs an $L_\infty$-algebra associated with any higher standard or twisted Courant algebroid (also known as a Vinogradov algebroid), and exhibits an explicit $L_\infty$-morphism from the Lie algebra associated with a standard Lie algebroid twisted by a closed 2-form to the Lie-2 algebra of the standard Courant algebroid. He poses the question of whether analogous canonical $L_\infty$-morphisms exist in higher degrees -- namely, for any standard higher Courant algebroid twisted by a closed $(r+1)$-form. We adfirmatively answer this question, presenting a general framework that naturally yields such canonical $L_\infty$-morphisms for arbitrary $r$, while at the same time clarifying the geometrical and homotopical structures underlying the construction. We also show how this framework accommodates the canonical morphism between Roger's observable $L_\infty$-algebra of a pre-$r$-plectic manifold and the higher Courant algebra described by Zambon and one of the authors in "Observables on multisymplectic manifolds and higher Courant algebroids" [arXiv:2209.05836]. |
| title | $L_\infty$-morphisms between twisted Courant $r$-Lie algebras and untwisted Courant $(r{+}1)$-Lie algebroids |
| topic | Symplectic Geometry Mathematical Physics Differential Geometry 53D05, 17B55 |
| url | https://arxiv.org/abs/2602.14702 |